## Representation of Cohomology of Hilbert Schemes of Points on K3
Surfaces

Letao Zhang, Rice

Let S be a K3 surface, and X denote the Hilbert scheme of n points
on S. X inherits lots of nice properties from S, such as smoothness,
symplectic form, and etc. One of the most interesting phenomena is that
H^k(X), for any pair of (k,n), is determined by some Heisenberg algebra
structure, and the the special orthogonal group action associated with the
intersection form on H^2(S) can be extended to H^k(X). My current work
focuses on using Representation Theory to see more patterns lying inside
H^k(X).